What is still missing? In order to complete the program of [1]} with our compact spectral triple, we need to prove
the second Connes' formula (which provides the link between the Chern character
and the Hall conductivity) and to introduce the (random) perturbation by
electrostatic potentials. The first question is related to the study of the
quantized calculus of the magnetic algebra \({C}_B\)  generated by the
differential (REF ). The second question consists of
replacing the magnetic algebra \({C}_B\) , which is a twisted group
\(C^*\) -algebra of \(\mathbb {R}^2\) , with a twisted \(C^*\) -crossed product generated by the
action of \(\mathbb {R}^2\)  on the hull of the potentials (see, e.g., [1]} and references therein). Both of these aspects will be investigated in an upcoming work.
